YES Problem: plus(x,0()) -> x plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(0()),y) -> y times(s(x),y) -> plus(y,times(x,y)) div(0(),y) -> 0() div(x,y) -> quot(x,y,y) quot(0(),s(y),z) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) quot(x,0(),s(z)) -> s(div(x,s(z))) div(div(x,y),z) -> div(x,times(y,z)) Proof: DP Processor: DPs: plus#(s(x),y) -> plus#(x,y) times#(s(x),y) -> times#(x,y) times#(s(x),y) -> plus#(y,times(x,y)) div#(x,y) -> quot#(x,y,y) quot#(s(x),s(y),z) -> quot#(x,y,z) quot#(x,0(),s(z)) -> div#(x,s(z)) div#(div(x,y),z) -> times#(y,z) div#(div(x,y),z) -> div#(x,times(y,z)) TRS: plus(x,0()) -> x plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(0()),y) -> y times(s(x),y) -> plus(y,times(x,y)) div(0(),y) -> 0() div(x,y) -> quot(x,y,y) quot(0(),s(y),z) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) quot(x,0(),s(z)) -> s(div(x,s(z))) div(div(x,y),z) -> div(x,times(y,z)) EDG Processor: DPs: plus#(s(x),y) -> plus#(x,y) times#(s(x),y) -> times#(x,y) times#(s(x),y) -> plus#(y,times(x,y)) div#(x,y) -> quot#(x,y,y) quot#(s(x),s(y),z) -> quot#(x,y,z) quot#(x,0(),s(z)) -> div#(x,s(z)) div#(div(x,y),z) -> times#(y,z) div#(div(x,y),z) -> div#(x,times(y,z)) TRS: plus(x,0()) -> x plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(0()),y) -> y times(s(x),y) -> plus(y,times(x,y)) div(0(),y) -> 0() div(x,y) -> quot(x,y,y) quot(0(),s(y),z) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) quot(x,0(),s(z)) -> s(div(x,s(z))) div(div(x,y),z) -> div(x,times(y,z)) graph: quot#(s(x),s(y),z) -> quot#(x,y,z) -> quot#(s(x),s(y),z) -> quot#(x,y,z) quot#(s(x),s(y),z) -> quot#(x,y,z) -> quot#(x,0(),s(z)) -> div#(x,s(z)) quot#(x,0(),s(z)) -> div#(x,s(z)) -> div#(x,y) -> quot#(x,y,y) quot#(x,0(),s(z)) -> div#(x,s(z)) -> div#(div(x,y),z) -> times#(y,z) quot#(x,0(),s(z)) -> div#(x,s(z)) -> div#(div(x,y),z) -> div#(x,times(y,z)) div#(div(x,y),z) -> div#(x,times(y,z)) -> div#(x,y) -> quot#(x,y,y) div#(div(x,y),z) -> div#(x,times(y,z)) -> div#(div(x,y),z) -> times#(y,z) div#(div(x,y),z) -> div#(x,times(y,z)) -> div#(div(x,y),z) -> div#(x,times(y,z)) div#(div(x,y),z) -> times#(y,z) -> times#(s(x),y) -> times#(x,y) div#(div(x,y),z) -> times#(y,z) -> times#(s(x),y) -> plus#(y,times(x,y)) div#(x,y) -> quot#(x,y,y) -> quot#(s(x),s(y),z) -> quot#(x,y,z) div#(x,y) -> quot#(x,y,y) -> quot#(x,0(),s(z)) -> div#(x,s(z)) times#(s(x),y) -> times#(x,y) -> times#(s(x),y) -> times#(x,y) times#(s(x),y) -> times#(x,y) -> times#(s(x),y) -> plus#(y,times(x,y)) times#(s(x),y) -> plus#(y,times(x,y)) -> plus#(s(x),y) -> plus#(x,y) plus#(s(x),y) -> plus#(x,y) -> plus#(s(x),y) -> plus#(x,y) SCC Processor: #sccs: 3 #rules: 6 #arcs: 16/64 DPs: quot#(s(x),s(y),z) -> quot#(x,y,z) quot#(x,0(),s(z)) -> div#(x,s(z)) div#(div(x,y),z) -> div#(x,times(y,z)) div#(x,y) -> quot#(x,y,y) TRS: plus(x,0()) -> x plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(0()),y) -> y times(s(x),y) -> plus(y,times(x,y)) div(0(),y) -> 0() div(x,y) -> quot(x,y,y) quot(0(),s(y),z) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) quot(x,0(),s(z)) -> s(div(x,s(z))) div(div(x,y),z) -> div(x,times(y,z)) Subterm Criterion Processor: simple projection: pi(div#) = 0 pi(quot#) = 0 problem: DPs: quot#(x,0(),s(z)) -> div#(x,s(z)) div#(x,y) -> quot#(x,y,y) TRS: plus(x,0()) -> x plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(0()),y) -> y times(s(x),y) -> plus(y,times(x,y)) div(0(),y) -> 0() div(x,y) -> quot(x,y,y) quot(0(),s(y),z) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) quot(x,0(),s(z)) -> s(div(x,s(z))) div(div(x,y),z) -> div(x,times(y,z)) Bounds Processor: bound: 2 enrichment: top-dp automaton: final states: {12} transitions: div0(12,12) -> 10* div0(10,10) -> 10* div0(10,12) -> 10* div0(12,10) -> 10* quot0(12,10,10) -> 10* quot0(12,12,10) -> 10* quot0(10,10,12) -> 10* quot0(10,12,12) -> 10* quot0(12,10,12) -> 10* quot0(12,12,12) -> 10* quot0(10,10,10) -> 10* quot0(10,12,10) -> 10* div{#,1}(12,14) -> 10* div{#,1}(10,14) -> 12,10 s1(10) -> 14* s1(12) -> 14* quot{#,1}(12,10,10) -> 12,10 quot{#,1}(10,12,12) -> 10* quot{#,1}(12,12,12) -> 10* quot{#,1}(10,10,10) -> 12,10 quot{#,2}(10,14,14) -> 12,10 quot{#,2}(12,14,14) -> 10* quot{#,0}(12,10,10) -> 12* quot{#,0}(12,12,10) -> 12* quot{#,0}(10,10,12) -> 12* quot{#,0}(10,12,12) -> 12* quot{#,0}(12,10,12) -> 12* quot{#,0}(12,12,12) -> 12* quot{#,0}(10,10,10) -> 12* quot{#,0}(10,12,10) -> 12* 00() -> 10* s0(10) -> 10* s0(12) -> 10* div{#,0}(10,10) -> 12,10 div{#,0}(10,12) -> 10* div{#,0}(12,10) -> 12,10 div{#,0}(12,12) -> 10* plus0(10,10) -> 10* plus0(10,12) -> 10* plus0(12,10) -> 10* plus0(12,12) -> 10* times0(12,12) -> 10* times0(10,10) -> 10* times0(10,12) -> 10* times0(12,10) -> 10* 12 -> 10* problem: DPs: quot#(x,0(),s(z)) -> div#(x,s(z)) TRS: plus(x,0()) -> x plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(0()),y) -> y times(s(x),y) -> plus(y,times(x,y)) div(0(),y) -> 0() div(x,y) -> quot(x,y,y) quot(0(),s(y),z) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) quot(x,0(),s(z)) -> s(div(x,s(z))) div(div(x,y),z) -> div(x,times(y,z)) Bounds Processor: bound: 0 enrichment: top-dp automaton: final states: {19} transitions: 00() -> 17,16,15,11 s0(15) -> 18* s0(17) -> 18* s0(19) -> 18* s0(14) -> 18* s0(16) -> 16,17,18 s0(11) -> 18* s0(18) -> 18* s0(13) -> 18* div{#,0}(17,14) -> 13* div{#,0}(17,16) -> 13* div{#,0}(17,18) -> 19* div{#,0}(18,11) -> 13* div{#,0}(13,11) -> 13* div{#,0}(18,13) -> 13* div{#,0}(13,13) -> 13* div{#,0}(18,15) -> 13* div{#,0}(13,15) -> 13* div{#,0}(18,17) -> 13* div{#,0}(13,17) -> 13* div{#,0}(18,19) -> 13* div{#,0}(13,19) -> 13* div{#,0}(19,14) -> 13* div{#,0}(14,14) -> 13* div{#,0}(19,16) -> 13* div{#,0}(14,16) -> 13* div{#,0}(19,18) -> 19* div{#,0}(14,18) -> 19* div{#,0}(15,11) -> 13* div{#,0}(15,13) -> 13* div{#,0}(15,15) -> 13* div{#,0}(15,17) -> 13* div{#,0}(15,19) -> 13* div{#,0}(16,14) -> 13* div{#,0}(11,14) -> 13* div{#,0}(16,16) -> 13* div{#,0}(11,16) -> 13* div{#,0}(16,18) -> 19* div{#,0}(11,18) -> 19* div{#,0}(17,11) -> 13* div{#,0}(17,13) -> 13* div{#,0}(17,15) -> 13* div{#,0}(17,17) -> 13* div{#,0}(17,19) -> 13* div{#,0}(18,14) -> 13* div{#,0}(13,14) -> 13* div{#,0}(18,16) -> 13* div{#,0}(13,16) -> 13* div{#,0}(18,18) -> 19* div{#,0}(13,18) -> 19* div{#,0}(19,11) -> 13* div{#,0}(14,11) -> 13* div{#,0}(19,13) -> 13* div{#,0}(14,13) -> 13* div{#,0}(19,15) -> 13* div{#,0}(14,15) -> 13* div{#,0}(19,17) -> 13* div{#,0}(14,17) -> 13* div{#,0}(19,19) -> 13* div{#,0}(14,19) -> 13* div{#,0}(15,14) -> 13* div{#,0}(15,16) -> 13* div{#,0}(15,18) -> 19* div{#,0}(16,11) -> 13* div{#,0}(11,11) -> 13* div{#,0}(16,13) -> 13* div{#,0}(11,13) -> 13* div{#,0}(16,15) -> 13* div{#,0}(11,15) -> 13* div{#,0}(16,17) -> 13* div{#,0}(11,17) -> 13* div{#,0}(16,19) -> 13* div{#,0}(11,19) -> 13* plus0(17,14) -> 14* plus0(17,16) -> 14* plus0(17,18) -> 14* plus0(18,11) -> 14* plus0(13,11) -> 14* plus0(18,13) -> 14* plus0(13,13) -> 14* plus0(18,15) -> 14* plus0(13,15) -> 14* plus0(18,17) -> 14* plus0(13,17) -> 14* plus0(18,19) -> 14* plus0(13,19) -> 14* plus0(19,14) -> 14* plus0(14,14) -> 14* plus0(19,16) -> 14* plus0(14,16) -> 14* plus0(19,18) -> 14* plus0(14,18) -> 14* plus0(15,11) -> 14* plus0(15,13) -> 14* plus0(15,15) -> 14* plus0(15,17) -> 14* plus0(15,19) -> 14* plus0(16,14) -> 14* plus0(11,14) -> 14* plus0(16,16) -> 14* plus0(11,16) -> 14* plus0(16,18) -> 14* plus0(11,18) -> 14* plus0(17,11) -> 14* plus0(17,13) -> 14* plus0(17,15) -> 14* plus0(17,17) -> 14* plus0(17,19) -> 14* plus0(18,14) -> 14* plus0(13,14) -> 14* plus0(18,16) -> 14* plus0(13,16) -> 14* plus0(18,18) -> 14* plus0(13,18) -> 14* plus0(19,11) -> 14* plus0(14,11) -> 14* plus0(19,13) -> 14* plus0(14,13) -> 14* plus0(19,15) -> 14* plus0(14,15) -> 14* plus0(19,17) -> 14* plus0(14,17) -> 14* plus0(19,19) -> 14* plus0(14,19) -> 14* plus0(15,14) -> 14* plus0(15,16) -> 14* plus0(15,18) -> 14* plus0(16,11) -> 14* plus0(11,11) -> 14* plus0(16,13) -> 14* plus0(11,13) -> 14* plus0(16,15) -> 14* plus0(11,15) -> 14* plus0(16,17) -> 14* plus0(11,17) -> 14* plus0(16,19) -> 14* plus0(11,19) -> 14* times0(17,14) -> 15* times0(17,16) -> 15* times0(17,18) -> 15* times0(18,11) -> 15* times0(13,11) -> 15* times0(18,13) -> 15* times0(13,13) -> 15* times0(18,15) -> 15* times0(13,15) -> 15* times0(18,17) -> 15* times0(13,17) -> 15* times0(18,19) -> 15* times0(13,19) -> 15* times0(19,14) -> 15* times0(14,14) -> 15* times0(19,16) -> 15* times0(14,16) -> 15* times0(19,18) -> 15* times0(14,18) -> 15* times0(15,11) -> 15* times0(15,13) -> 15* times0(15,15) -> 15* times0(15,17) -> 15* times0(15,19) -> 15* times0(16,14) -> 15* times0(11,14) -> 15* times0(16,16) -> 15* times0(11,16) -> 15* times0(16,18) -> 15* times0(11,18) -> 15* times0(17,11) -> 15* times0(17,13) -> 15* times0(17,15) -> 15* times0(17,17) -> 15* times0(17,19) -> 15* times0(18,14) -> 15* times0(13,14) -> 15* times0(18,16) -> 15* times0(13,16) -> 15* times0(18,18) -> 15* times0(13,18) -> 15* times0(19,11) -> 15* times0(14,11) -> 15* times0(19,13) -> 15* times0(14,13) -> 15* times0(19,15) -> 15* times0(14,15) -> 15* times0(19,17) -> 15* times0(14,17) -> 15* times0(19,19) -> 15* times0(14,19) -> 15* times0(15,14) -> 15* times0(15,16) -> 15* times0(15,18) -> 15* times0(16,11) -> 15* times0(11,11) -> 15* times0(16,13) -> 15* times0(11,13) -> 15* times0(16,15) -> 15* times0(11,15) -> 15* times0(16,17) -> 15* times0(11,17) -> 15* times0(16,19) -> 15* times0(11,19) -> 15* div0(17,14) -> 16* div0(17,16) -> 16* div0(17,18) -> 16* div0(18,11) -> 16* div0(13,11) -> 16* div0(18,13) -> 16* div0(13,13) -> 16* div0(18,15) -> 16* div0(13,15) -> 16* div0(18,17) -> 16* div0(13,17) -> 16* div0(18,19) -> 16* div0(13,19) -> 16* div0(19,14) -> 16* div0(14,14) -> 16* div0(19,16) -> 16* div0(14,16) -> 16* div0(19,18) -> 16* div0(14,18) -> 16* div0(15,11) -> 16* div0(15,13) -> 16* div0(15,15) -> 16* div0(15,17) -> 16* div0(15,19) -> 16* div0(16,14) -> 16* div0(11,14) -> 16* div0(16,16) -> 16* div0(11,16) -> 16* div0(16,18) -> 16* div0(11,18) -> 16* div0(17,11) -> 16* div0(17,13) -> 16* div0(17,15) -> 16* div0(17,17) -> 16* div0(17,19) -> 16* div0(18,14) -> 16* div0(13,14) -> 16* div0(18,16) -> 16* div0(13,16) -> 16* div0(18,18) -> 16* div0(13,18) -> 16* div0(19,11) -> 16* div0(14,11) -> 16* div0(19,13) -> 16* div0(14,13) -> 16* div0(19,15) -> 16* div0(14,15) -> 16* div0(19,17) -> 16* div0(14,17) -> 16* div0(19,19) -> 16* div0(14,19) -> 16* div0(15,14) -> 16* div0(15,16) -> 16* div0(15,18) -> 16* div0(16,11) -> 16* div0(11,11) -> 16* div0(16,13) -> 16* div0(11,13) -> 16* div0(16,15) -> 16* div0(11,15) -> 16* div0(16,17) -> 16* div0(11,17) -> 16* div0(16,19) -> 16* div0(11,19) -> 16* quot0(13,14,17) -> 17* quot0(17,14,16) -> 17* quot0(16,16,15) -> 17* quot0(15,18,14) -> 17* quot0(19,19,19) -> 17* quot0(11,11,18) -> 17* quot0(14,13,16) -> 17* quot0(13,15,15) -> 17* quot0(11,19,13) -> 17* quot0(16,18,19) -> 17* quot0(19,11,15) -> 17* quot0(18,13,14) -> 17* quot0(17,15,13) -> 17* quot0(13,17,19) -> 17* quot0(14,14,13) -> 17* quot0(17,16,11) -> 17* quot0(19,13,19) -> 17* quot0(18,15,18) -> 17* quot0(17,17,17) -> 17* quot0(11,13,13) -> 17* quot0(14,15,11) -> 17* quot0(15,14,18) -> 17* quot0(14,16,17) -> 17* quot0(18,16,16) -> 17* quot0(17,18,15) -> 17* quot0(11,14,11) -> 17* quot0(13,11,19) -> 17* quot0(11,15,17) -> 17* quot0(15,15,16) -> 17* quot0(14,17,15) -> 17* quot0(13,19,14) -> 17* quot0(11,16,15) -> 17* quot0(17,11,17) -> 17* quot0(19,15,14) -> 17* quot0(18,17,13) -> 17* quot0(14,19,19) -> 17* quot0(16,14,14) -> 17* quot0(15,16,13) -> 17* quot0(18,18,11) -> 17* quot0(11,18,19) -> 17* quot0(19,17,18) -> 17* quot0(18,19,17) -> 17* quot0(14,11,15) -> 17* quot0(13,13,14) -> 17* quot0(15,17,11) -> 17* quot0(17,14,19) -> 17* quot0(16,16,18) -> 17* quot0(15,18,17) -> 17* quot0(19,18,16) -> 17* quot0(18,11,13) -> 17* quot0(14,13,19) -> 17* quot0(13,15,18) -> 17* quot0(16,17,16) -> 17* quot0(15,19,15) -> 17* quot0(13,16,16) -> 17* quot0(19,11,18) -> 17* quot0(18,13,17) -> 17* quot0(19,19,13) -> 17* quot0(15,11,11) -> 17* quot0(18,14,15) -> 17* quot0(17,16,14) -> 17* quot0(16,18,13) -> 17* quot0(16,11,16) -> 17* quot0(15,13,15) -> 17* quot0(14,15,14) -> 17* quot0(13,17,13) -> 17* quot0(16,19,11) -> 17* quot0(18,16,19) -> 17* quot0(17,18,18) -> 17* quot0(11,14,14) -> 17* quot0(13,18,11) -> 17* quot0(19,13,13) -> 17* quot0(15,15,19) -> 17* quot0(14,17,18) -> 17* quot0(13,19,17) -> 17* quot0(17,19,16) -> 17* quot0(19,14,11) -> 17* quot0(11,16,18) -> 17* quot0(14,18,16) -> 17* quot0(19,15,17) -> 17* quot0(13,11,13) -> 17* quot0(16,13,11) -> 17* quot0(11,17,16) -> 17* quot0(16,14,17) -> 17* quot0(19,16,15) -> 17* quot0(18,18,14) -> 17* quot0(14,11,18) -> 17* quot0(13,13,17) -> 17* quot0(17,13,16) -> 17* quot0(16,15,15) -> 16,17 quot0(15,17,14) -> 17* quot0(14,19,13) -> 17* quot0(19,18,19) -> 17* quot0(13,14,15) -> 17* quot0(11,18,13) -> 17* quot0(16,17,19) -> 17* quot0(15,19,18) -> 17* quot0(11,11,16) -> 17* quot0(11,19,11) -> 17* quot0(17,14,13) -> 17* quot0(13,16,19) -> 17* quot0(15,11,14) -> 17* quot0(14,13,13) -> 17* quot0(17,15,11) -> 17* quot0(18,14,18) -> 17* quot0(17,16,17) -> 17* quot0(14,14,11) -> 17* quot0(16,11,19) -> 17* quot0(15,13,18) -> 17* quot0(14,15,17) -> 17* quot0(18,15,16) -> 17* quot0(17,17,15) -> 17* quot0(16,19,14) -> 17* quot0(11,13,11) -> 17* quot0(11,14,17) -> 17* quot0(15,14,16) -> 17* quot0(14,16,15) -> 17* quot0(13,18,14) -> 17* quot0(17,19,19) -> 17* quot0(11,15,15) -> 16,17 quot0(19,14,14) -> 17* quot0(18,16,13) -> 17* quot0(14,18,19) -> 17* quot0(17,11,15) -> 17* quot0(16,13,14) -> 17* quot0(15,15,13) -> 17* quot0(18,17,11) -> 17* quot0(11,17,19) -> 17* quot0(19,16,18) -> 17* quot0(18,18,17) -> 17* quot0(15,16,11) -> 17* quot0(17,13,19) -> 17* quot0(16,15,18) -> 17* quot0(15,17,17) -> 17* quot0(19,17,16) -> 17* quot0(18,19,15) -> 17* quot0(13,14,18) -> 17* quot0(16,16,16) -> 17* quot0(15,18,15) -> 17* quot0(18,11,11) -> 17* quot0(11,11,19) -> 17* quot0(13,15,16) -> 17* quot0(11,19,14) -> 17* quot0(19,18,13) -> 17* quot0(15,11,17) -> 17* quot0(19,11,16) -> 17* quot0(18,13,15) -> 17* quot0(17,15,14) -> 17* quot0(16,17,13) -> 17* quot0(19,19,11) -> 17* quot0(14,14,14) -> 17* quot0(13,16,13) -> 17* quot0(16,18,11) -> 17* quot0(18,15,19) -> 17* quot0(17,17,18) -> 17* quot0(16,19,17) -> 17* quot0(11,13,14) -> 17* quot0(13,17,11) -> 17* quot0(15,14,19) -> 17* quot0(14,16,18) -> 17* quot0(13,18,17) -> 17* quot0(17,18,16) -> 17* quot0(16,11,13) -> 17* quot0(19,13,11) -> 17* quot0(11,15,18) -> 17* quot0(14,17,16) -> 17* quot0(13,19,15) -> 17* quot0(19,14,17) -> 17* quot0(11,16,16) -> 17* quot0(17,11,18) -> 17* quot0(16,13,17) -> 17* quot0(19,15,15) -> 17* quot0(18,17,14) -> 17* quot0(17,19,13) -> 17* quot0(13,11,11) -> 17* quot0(16,14,15) -> 17* quot0(15,16,14) -> 17* quot0(14,18,13) -> 17* quot0(19,17,19) -> 17* quot0(18,19,18) -> 17* quot0(14,11,16) -> 17* quot0(13,13,15) -> 17* quot0(11,17,13) -> 17* quot0(14,19,11) -> 17* quot0(16,16,19) -> 17* quot0(15,18,18) -> 16,17 quot0(11,18,11) -> 17* quot0(18,11,14) -> 17* quot0(17,13,13) -> 17* quot0(13,15,19) -> 17* quot0(11,19,17) -> 17* quot0(15,19,16) -> 17* quot0(17,14,11) -> 17* quot0(19,11,19) -> 17* quot0(18,13,18) -> 17* quot0(17,15,17) -> 17* quot0(19,19,14) -> 17* quot0(11,11,13) -> 17* quot0(14,13,11) -> 17* quot0(14,14,17) -> 17* quot0(18,14,16) -> 17* quot0(17,16,15) -> 17* quot0(16,18,14) -> 17* quot0(11,13,17) -> 17* quot0(15,13,16) -> 17* quot0(14,15,15) -> 17* quot0(13,17,14) -> 17* quot0(17,18,19) -> 17* quot0(11,14,15) -> 17* quot0(19,13,14) -> 17* quot0(18,15,13) -> 17* quot0(14,17,19) -> 17* quot0(13,19,18) -> 17* quot0(15,14,13) -> 17* quot0(18,16,11) -> 17* quot0(11,16,19) -> 17* quot0(19,15,18) -> 17* quot0(18,17,17) -> 17* quot0(13,11,14) -> 17* quot0(15,15,11) -> 17* quot0(16,14,18) -> 17* quot0(15,16,17) -> 17* quot0(19,16,16) -> 17* quot0(18,18,15) -> 17* quot0(14,11,19) -> 17* quot0(13,13,18) -> 17* quot0(16,15,16) -> 17* quot0(15,17,15) -> 17* quot0(14,19,14) -> 17* quot0(13,14,16) -> 17* quot0(11,18,14) -> 17* quot0(18,11,17) -> 17* quot0(19,17,13) -> 17* quot0(15,19,19) -> 17* quot0(17,14,14) -> 17* quot0(16,16,13) -> 17* quot0(19,18,11) -> 17* quot0(19,19,17) -> 17* quot0(15,11,15) -> 17* quot0(14,13,14) -> 17* quot0(13,15,13) -> 17* quot0(16,17,11) -> 17* quot0(18,14,19) -> 17* quot0(17,16,18) -> 17* quot0(16,18,17) -> 17* quot0(13,16,11) -> 17* quot0(19,11,13) -> 17* quot0(15,13,19) -> 17* quot0(14,15,18) -> 17* quot0(13,17,17) -> 17* quot0(17,17,16) -> 17* quot0(16,19,15) -> 17* quot0(11,14,18) -> 17* quot0(14,16,16) -> 17* quot0(13,18,15) -> 17* quot0(19,13,17) -> 17* quot0(16,11,11) -> 17* quot0(11,15,16) -> 17* quot0(19,14,15) -> 17* quot0(18,16,14) -> 17* quot0(17,18,13) -> 17* quot0(13,11,17) -> 17* quot0(17,11,16) -> 17* quot0(16,13,15) -> 17* quot0(15,15,14) -> 17* quot0(14,17,13) -> 17* quot0(17,19,11) -> 17* quot0(19,16,19) -> 17* quot0(18,18,18) -> 17* quot0(11,16,13) -> 17* quot0(14,18,11) -> 17* quot0(16,15,19) -> 17* quot0(15,17,18) -> 17* quot0(14,19,17) -> 17* quot0(18,19,16) -> 17* quot0(11,17,11) -> 17* quot0(13,14,19) -> 17* quot0(11,18,17) -> 17* quot0(15,18,16) -> 17* quot0(14,11,13) -> 17* quot0(17,13,11) -> 17* quot0(11,19,15) -> 17* quot0(17,14,17) -> 17* quot0(19,18,14) -> 17* quot0(15,11,18) -> 17* quot0(14,13,17) -> 17* quot0(18,13,16) -> 17* quot0(17,15,15) -> 17* quot0(16,17,14) -> 17* quot0(15,19,13) -> 17* quot0(11,11,11) -> 17* quot0(14,14,15) -> 17* quot0(13,16,14) -> 17* quot0(17,17,19) -> 17* quot0(16,19,18) -> 17* quot0(11,13,15) -> 17* quot0(18,14,13) -> 17* quot0(14,16,19) -> 17* quot0(13,18,18) -> 17* quot0(16,11,14) -> 17* quot0(15,13,13) -> 17* quot0(18,15,11) -> 17* quot0(11,15,19) -> 17* quot0(13,19,16) -> 17* quot0(19,14,18) -> 17* quot0(18,16,17) -> 17* quot0(15,14,11) -> 17* quot0(17,11,19) -> 17* quot0(16,13,18) -> 17* quot0(15,15,17) -> 17* quot0(19,15,16) -> 17* quot0(18,17,15) -> 17* quot0(17,19,14) -> 17* quot0(16,14,16) -> 17* quot0(15,16,15) -> 17* quot0(14,18,14) -> 17* quot0(18,19,19) -> 17* quot0(13,13,16) -> 17* quot0(11,17,14) -> 17* quot0(19,16,13) -> 17* quot0(15,18,19) -> 17* quot0(18,11,15) -> 17* quot0(17,13,14) -> 17* quot0(16,15,13) -> 17* quot0(19,17,11) -> 17* quot0(11,19,18) -> 17* quot0(19,18,17) -> 17* quot0(13,14,13) -> 17* quot0(16,16,11) -> 17* quot0(18,13,19) -> 17* quot0(17,15,18) -> 17* quot0(16,17,17) -> 16,17 quot0(19,19,15) -> 17* quot0(11,11,14) -> 17* quot0(13,15,11) -> 17* quot0(14,14,18) -> 17* quot0(13,16,17) -> 17* quot0(17,16,16) -> 17* quot0(16,18,15) -> 17* quot0(19,11,11) -> 17* quot0(11,13,18) -> 17* quot0(14,15,16) -> 17* quot0(13,17,15) -> 17* quot0(11,14,16) -> 17* quot0(16,11,17) -> 17* quot0(19,13,15) -> 17* quot0(18,15,14) -> 17* quot0(17,17,13) -> 17* quot0(13,19,19) -> 17* quot0(15,14,14) -> 16,17 quot0(14,16,13) -> 17* quot0(17,18,11) -> 17* quot0(19,15,19) -> 17* quot0(18,17,18) -> 17* quot0(17,19,17) -> 17* quot0(13,11,15) -> 17* quot0(11,15,13) -> 17* quot0(14,17,11) -> 17* quot0(16,14,19) -> 17* quot0(15,16,18) -> 17* quot0(14,18,17) -> 17* quot0(18,18,16) -> 17* quot0(11,16,11) -> 17* quot0(17,11,13) -> 17* quot0(13,13,19) -> 17* quot0(11,17,17) -> 16,17 quot0(15,17,16) -> 17* quot0(14,19,15) -> 17* quot0(11,18,15) -> 17* quot0(18,11,18) -> 17* quot0(17,13,17) -> 17* quot0(19,17,14) -> 17* quot0(18,19,13) -> 17* quot0(14,11,11) -> 17* quot0(17,14,15) -> 17* quot0(16,16,14) -> 17* quot0(15,18,13) -> 17* quot0(19,19,18) -> 17* quot0(11,11,17) -> 17* quot0(15,11,16) -> 17* quot0(14,13,15) -> 17* quot0(13,15,14) -> 17* quot0(15,19,11) -> 17* quot0(17,16,19) -> 17* quot0(16,18,18) -> 17* quot0(19,11,14) -> 17* quot0(18,13,13) -> 17* quot0(14,15,19) -> 17* quot0(13,17,18) -> 17* quot0(16,19,16) -> 17* quot0(18,14,11) -> 17* quot0(11,14,19) -> 17* quot0(13,18,16) -> 17* quot0(19,13,18) -> 17* quot0(18,15,17) -> 17* quot0(15,13,11) -> 17* quot0(15,14,17) -> 17* quot0(19,14,16) -> 17* quot0(18,16,15) -> 17* quot0(17,18,14) -> 17* quot0(13,11,18) -> 17* quot0(16,13,16) -> 17* quot0(15,15,15) -> 17* quot0(14,17,14) -> 17* quot0(13,19,13) -> 17* quot0(18,18,19) -> 17* quot0(11,16,14) -> 17* quot0(19,15,13) -> 17* quot0(15,17,19) -> 17* quot0(14,19,18) -> 17* quot0(16,14,13) -> 17* quot0(19,16,11) -> 17* quot0(11,18,18) -> 17* quot0(19,17,17) -> 17* quot0(14,11,14) -> 17* quot0(13,13,13) -> 17* quot0(16,15,11) -> 17* quot0(11,19,16) -> 17* quot0(17,14,18) -> 17* quot0(16,16,17) -> 17* quot0(19,18,15) -> 17* quot0(13,14,11) -> 17* quot0(15,11,19) -> 17* quot0(14,13,18) -> 17* quot0(13,15,17) -> 17* quot0(17,15,16) -> 17* quot0(16,17,15) -> 17* quot0(15,19,14) -> 17* quot0(14,14,16) -> 17* quot0(13,16,15) -> 17* quot0(19,11,17) -> 17* quot0(16,19,19) -> 16,17 quot0(11,13,16) -> 17* quot0(18,14,14) -> 17* quot0(17,16,13) -> 17* quot0(13,18,19) -> 17* quot0(16,11,15) -> 17* quot0(15,13,14) -> 17* quot0(14,15,13) -> 17* quot0(17,17,11) -> 17* quot0(19,14,19) -> 17* quot0(18,16,18) -> 17* quot0(17,18,17) -> 17* quot0(11,14,13) -> 17* quot0(14,16,11) -> 17* quot0(16,13,19) -> 17* quot0(15,15,18) -> 17* quot0(14,17,17) -> 17* quot0(18,17,16) -> 17* quot0(17,19,15) -> 17* quot0(11,15,11) -> 17* quot0(11,16,17) -> 17* quot0(15,16,16) -> 16,17 quot0(14,18,15) -> 17* quot0(17,11,11) -> 17* quot0(11,17,15) -> 17* quot0(19,16,14) -> 17* quot0(18,18,13) -> 17* quot0(14,11,17) -> 17* quot0(18,11,16) -> 17* quot0(17,13,15) -> 17* quot0(16,15,14) -> 17* quot0(15,17,13) -> 17* quot0(18,19,11) -> 17* quot0(11,19,19) -> 16,17 quot0(19,18,18) -> 17* quot0(13,14,14) -> 17* quot0(15,18,11) -> 17* quot0(17,15,19) -> 17* quot0(16,17,18) -> 17* quot0(15,19,17) -> 17* quot0(19,19,16) -> 17* quot0(11,11,15) -> 17* quot0(14,14,19) -> 17* quot0(13,16,18) -> 17* quot0(16,18,16) -> 17* quot0(15,11,13) -> 17* quot0(18,13,11) -> 17* quot0(11,13,19) -> 17* quot0(13,17,16) -> 17* quot0(18,14,17) -> 17* quot0(16,11,18) -> 17* quot0(15,13,17) -> 17* quot0(19,13,16) -> 17* quot0(18,15,15) -> 17* quot0(17,17,14) -> 17* quot0(16,19,13) -> 17* quot0(15,14,15) -> 17* quot0(14,16,14) -> 17* quot0(13,18,13) -> 17* quot0(18,17,19) -> 17* quot0(17,19,18) -> 17* quot0(13,11,16) -> 17* quot0(11,15,14) -> 17* quot0(13,19,11) -> 17* quot0(19,14,13) -> 17* quot0(15,16,19) -> 17* quot0(14,18,18) -> 17* quot0(17,11,14) -> 17* quot0(16,13,13) -> 17* quot0(19,15,11) -> 17* quot0(11,17,18) -> 17* quot0(14,19,16) -> 17* quot0(19,16,17) -> 17* quot0(16,14,11) -> 17* quot0(11,18,16) -> 17* quot0(18,11,19) -> 17* quot0(17,13,18) -> 17* quot0(16,15,17) -> 17* quot0(19,17,15) -> 17* quot0(18,19,14) -> 17* quot0(13,13,11) -> 17* 11 -> 14* 13 -> 14* 14 -> 15* 15 -> 14* 16 -> 15,14 17 -> 14* 18 -> 15,14 19 -> 14* problem: DPs: TRS: plus(x,0()) -> x plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(0()),y) -> y times(s(x),y) -> plus(y,times(x,y)) div(0(),y) -> 0() div(x,y) -> quot(x,y,y) quot(0(),s(y),z) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) quot(x,0(),s(z)) -> s(div(x,s(z))) div(div(x,y),z) -> div(x,times(y,z)) Qed DPs: times#(s(x),y) -> times#(x,y) TRS: plus(x,0()) -> x plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(0()),y) -> y times(s(x),y) -> plus(y,times(x,y)) div(0(),y) -> 0() div(x,y) -> quot(x,y,y) quot(0(),s(y),z) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) quot(x,0(),s(z)) -> s(div(x,s(z))) div(div(x,y),z) -> div(x,times(y,z)) Subterm Criterion Processor: simple projection: pi(times#) = 0 problem: DPs: TRS: plus(x,0()) -> x plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(0()),y) -> y times(s(x),y) -> plus(y,times(x,y)) div(0(),y) -> 0() div(x,y) -> quot(x,y,y) quot(0(),s(y),z) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) quot(x,0(),s(z)) -> s(div(x,s(z))) div(div(x,y),z) -> div(x,times(y,z)) Qed DPs: plus#(s(x),y) -> plus#(x,y) TRS: plus(x,0()) -> x plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(0()),y) -> y times(s(x),y) -> plus(y,times(x,y)) div(0(),y) -> 0() div(x,y) -> quot(x,y,y) quot(0(),s(y),z) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) quot(x,0(),s(z)) -> s(div(x,s(z))) div(div(x,y),z) -> div(x,times(y,z)) Subterm Criterion Processor: simple projection: pi(plus#) = 0 problem: DPs: TRS: plus(x,0()) -> x plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) times(0(),y) -> 0() times(s(0()),y) -> y times(s(x),y) -> plus(y,times(x,y)) div(0(),y) -> 0() div(x,y) -> quot(x,y,y) quot(0(),s(y),z) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) quot(x,0(),s(z)) -> s(div(x,s(z))) div(div(x,y),z) -> div(x,times(y,z)) Qed